Question: Simplify the following expression: $t = \dfrac{-28k^2 + 8k}{-24k}$ You can assume $k \neq 0$.
Answer: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $-28k^2 + 8k = - (2\cdot2\cdot7 \cdot k \cdot k) + (2\cdot2\cdot2 \cdot k)$ The denominator can be factored: $-24k = - (2\cdot2\cdot2\cdot3 \cdot k)$ The greatest common factor of all the terms is $4k$ Factoring out $4k$ gives us: $t = \dfrac{(4k)(-7k + 2)}{(4k)(-6)}$ Dividing both the numerator and denominator by $4k$ gives: $t = \dfrac{-7k + 2}{-6}$